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CMPSCI 187
Introduction to Programming
with Data Structures
Computer Science 187
Lecture 17: Implementing Trees
Announcements
1. Current OWL and project 4 are due
today (November 8).
2. New programming project up soon.
3. New OWL up soon.
1
CMPSCI 187
General Tree Interfaces
General Tree Interface


Interface for traversals
of general trees
public interface TreeInterface
public interface TreeIteratorInterface
{
{
public Object getData();
public Iterator PreorderIterator();
public int getHeight();
public Iterator PostOrderIterator();
public int getNumberOfNodes();
public Iterator InorderIterator();
public boolean isEmpty();
public Iterator LevelOrderIterator();
public void clear();
}
}
2
CMPSCI 187
Binary Tree interface
methods only
public Object getData();
public int getHeight();
public int getNumberOfNodes();
public boolean isEmpty();
public void clear();
public void setTree(Object rootData);
public void setTree(Object rootData, BinaryTreeInterface
leftTree, BinaryTreeInterface rightTree);
public Iterator PreorderIterator();
public Iterator PostOrderIterator();
public Iterator InorderIterator();
public Iterator LevelOrderIterator();
3
CMPSCI 187
The Binary Tree Interface
public interface BinaryTreeInterface extends
TreeInterface, TreeIteratorInterface
{
public void setTree(Object rootData);
public void setTree(Object rootData, BinaryTreeInterface
leftTree, BinaryTreeInterface rightTree);
}//end BinaryTreeInterface
Exceptions?
4
CMPSCI 187
…and recall our Binary Tree Node Interface
public interface BinaryNodeInterface
{
public Object getData(); //returns the data element at this node.
public void setData(Object myElement); //sets data element to myElement
public void setLeftChild(BinaryNodeInterface myLeft); //set left child to myLeft
public void setRightChild(BinaryNodeInterface myRight); //set right child to myRight
public BinaryNodeInterface getLeftChild(); //returns left child node
public BinaryNodeInterface getRightChild(); //returns right child node
public boolean hasLeftChild(); //returns true if this node has a left child
public boolean hasRightChild(); //returns true if this node has a right child
public boolean isLeaf(); //returns true if node is a leaf node.
}
5
CMPSCI 187
The methods of the interfaces
BinaryTreeInterface
BinaryNodeInterface
public Object getData();
public Object getData();
public int getHeight();
public void setData(Object myElement);
public int getNumberOfNodes();
public void setLeftChild(BinaryNodeInterface myLeft);
public boolean isEmpty();
public void setRightChild(BinaryNodeInterface myRight);
public void clear();
public BinaryNodeInterface getLeftChild();
public void setTree(Object rootData);
public BinaryNodeInterface getRightChild();
public void setTree(Object rootData,
public boolean hasLeftChild();
BinaryTreeInterface leftTree,
public boolean hasRightChild();
BinaryTreeInterface rightTree);
public boolean isLeaf();
public Iterator PreorderIterator();
public Iterator PostOrderIterator();
public Iterator InorderIterator();
public Iterator LevelOrderIterator();
6
CMPSCI 187
An Example Program
public class BinaryTreeTest
{
public static void main (String args[]) throws BinaryTreeException
{
BinaryTree t = new BinaryTree(new Integer(1));
System.out.println("Element at root of tree =
" + t.getData());
System.out.println(”Tree t is: ");
t.inorderTraverse();
System.out.println();
BinaryTree tree1 = new BinaryTree();
tree1.setTree(new Integer(2),
new BinaryTree(new Integer (4)),
new BinaryTree(new Integer (5)));
System.out.println("Tree1 is: ");
tree1.inorderTraverse();
System.out.println();
t:
tree1:
4
1
2
5
7
CMPSCI 187
Example, cont'd.
BinaryTree tree2 = new BinaryTree();
tree2.setTree(new Integer (6),
new BinaryTree(new Integer(7)),
new BinaryTree(new Integer(8)));
System.out.println("tree2 is: ");
tree2.inorderTraverse();
System.out.println();
7
8
3
tree3:
6
BinaryTree tree3 = new BinaryTree();
tree3.setTree(new Integer(3), tree2, null);
System.out.println("Tree3 is: ");
tree3.inorderTraverse();
System.out.println();
BinaryTree tree4=new BinaryTree();
tree4.setTree(new Integer (1), tree1, tree3);
System.out.println("Final tree is: ");
tree4.inorderTraverse();
System.out.println();
}}
6
tree2:
7
tree4:
8
1
2
4
3
5
6
7
8
8
CMPSCI 187
Using ‘attach’
//tree4.setTree(new Integer (1), tree1, tree3);
BinaryTree tree4=new BinaryTree(new Integer(1));
tree4.attachLeft(tree1);
tree4.attachRight(tree3);
System.out.println("Final tree is: ");
tree4:
tree4.inorderTraverse();
System.out.println();
2
4
1
3
5
6
7
8
9
CMPSCI 187
Something to keep in mind…
BinaryNode N = tree3.getRoot();
N.setData(new Integer(1000));
System.out.println("Tree4 after changing
the data in the root node of tree3");
tree4.inorderTraverse();
System.out.println();
tree4:
1
2
What’s the output?
4
3
5
6
7
8
10
CMPSCI 187


Traversing a tree
Suppose I wanted to ‘visit’ all the nodes in this tree.
Furthermore, suppose I wanted to perform some
operation on the data there (such as printing it out).
root
A
B
C
D
H

E
I
J
F
K
G
L
What are some of the possible visitation patterns we
could use?
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CMPSCI 187
Tree Traversal Patterns
root

A
1
A Possible Pattern
B
2
 Touch* Root Node
 Visit Left subtree
D
3
 Visit Right subtree

Must be applied at
all levels of the
tree.

C
9
H
4
E
6
I
5
J
7
F
10
K
8
G
11
L
12
Called a PreOrder Traversal
*”touch” means doing something at the node, such as printing the element there.
12
CMPSCI 187
preorderTraverse( )
public void preorderTraverse()
{ preorderTraverse(root);}
t:
1
2
private void preorderTraverse(BinaryNode node)
{
4
if (node != null)
{
System.out.print(node.getData()+" ");
preorderTraverse((BinaryNode)node.getLeftChild());
preorderTraverse((BinaryNode)node.getRightChild());
Note the casts…..
}
}
3
5
6
7
8
Print tree using preorder traversal:
1 2 4 5 3 6 7 8
13
CMPSCI 187
Tree Traversal Patterns
root

A
8
A Possible Pattern
 Visit Left subtree
B
4
 Touch Root node
 Visit Right subtree

Must be applied at all
levels of the tree.

C
10
D
2
H
1
E
6
I
3
J
5
F
9
K
7
G
11
L
12
Called an InOrder Traversal
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CMPSCI 187
inorderTraverse()
public void inorderTraverse()
{ inorderTraverse(root);}
t:
1
2
private void inorderTraverse(BinaryNode node)
4
{
if (node != null)
{
inorderTraverse((BinaryNode)node.getLeftChild());
System.out.print(node.getData()+" ");
inorderTraverse((BinaryNode)node.getRightChild());
}
}
3
5
6
7
Print tree using inorder traversal:
4 2 5 1 7 6 8 3
8
15
CMPSCI 187
Tree Traversal Patterns
root

A
A Possible Pattern
12
B
7
 Visit Left subtree
 Visit Right subtree
D
3
 Touch Root Node

Must be applied at
all levels of the
tree.

C
11
H
1
E
6
I
2
J
4
F
8
K
5
G
10
L
9
Called a PostOrder Traversal
16
CMPSCI 187
postorderTraverse( )
public void postorderTraverse()
{ postorderTraverse(root);}
t:
1
2
private void postorderTraverse(BinaryNode node)
4
{
if (node != null)
{
postorderTraverse((BinaryNode)node.getLeftChild());
postorderTraverse((BinaryNode)node.getRightChild());
System.out.print(node.getData()+” “);
}
}
3
5
6
7
8
Print tree using postorder traversal:
4 5 2 7 8 6 3 1
17
CMPSCI 187
The BinaryNode Class
public class BinaryNode implements BinaryNodeInterface
{ private Object data;
private BinaryNode left;
private BinaryNode right;
//Constructors
public BinaryNode()
{this(null);}
public BinaryNode(Object dataPortion)
{ this(dataPortion, null,null); }
public BinaryNode(Object nodeData, BinaryNode leftChild,
BinaryNode rightChild)
{ data = nodeData;
left = leftChild;
18
right = rightChild;}
CMPSCI 187
The BinaryNode Class
public boolean isLeaf()
{ return ((left == null) && (right == null)); }
public Object getData()
{ return data;}
public void setData(Object newData)
{ data=newData;}
public void setLeftChild(BinaryNodeInterface leftChild)
{ left = (BinaryNode) leftChild;}
public BinaryNodeInterface getLeftChild()
{ return left;}
19
CMPSCI 187
The BinaryNode Class
public void setRightChild(BinaryNodeInterface
rightChild)
{ right = (BinaryNode) rightChild;}
public BinaryNodeInterface getRightChild()
{ return right;}
public boolean hasLeftChild()
{ return left != null; }
public boolean hasRightChild()
{ return right != null; }
}//end Binary Node
20
CMPSCI 187
The BinaryTree Class
import java.util.*
public class BinaryTree implements BinaryTreeInterface,
java.io.Serializable
{
//Implements a binary tree using the BinaryNode class
protected BinaryNode root;
••
•
21
CMPSCI 187
The BinaryTree Class:
Constructors
//The Constructors
public BinaryTree()
{ root = null; }
public BinaryTree(Object rootData)
{ root = new BinaryNode(rootData, null, null);}
public BinaryTree(Object rootData, BinaryTree leftTree,
BinaryTree rightTree)
{privateSetTree(rootData, leftTree, rightTree);}
••
•
22
The BinaryTree Class:
CMPSCI 187
getRootData
public Object getRootData()
{ Object rootData = null;
if (root != null) rootData=root.getData();
return rootData; }
public Object getRootData();
public int getHeight();
public int getNumberOfNodes();
public boolean isEmpty();
public void clear();
public void setTree(Object rootData);
public void setTree(Object rootData, BinaryTreeInterface
leftTree, BinaryTreeInterface rightTree);
public Iterator getPreorderIterator();
public Iterator getPostOrderIterator();
Null data at root or
no root at all?
EXCEPTIONS????
public Iterator getInorderIterator();
public Iterator getLevelOrderIterator();
23
CMPSCI 187
The getHeight() method

getHeight() should be a tree
method e.g. T.getHeight()
public int getHeight()
{
return getHeight(root);
}

getHeight() needs to have a
node as an argument to
support recursion
Notice
the structure:
 getHeight() is a public
tree method
 getHeight(node) is a private
method that takes a node
as an argument
We should use this mechanism on MOST tree methods that need a node argument.
24
CMPSCI 187
The BinaryTree Class:
getHeight


Recall that the height of a tree is the same as the depth of the
deepest node in the tree.
The height of a tree rooted at a node is 1 + max(height of left
tree, height of right tree) [RECURSIVE]
public Object getRootData();
public int getHeight()
{return getHeight(root);}
public int getHeight();
public int getNumberOfNodes();
public boolean isEmpty();
public void clear();
public void setTree(Object rootData);
public void setTree(Object rootData,
BinaryTreeInterface leftTree,
BinaryTreeInterface rightTree);
public Iterator getPreorderIterator();
public Iterator getPostOrderIterator();
public Iterator getInorderIterator();
public Iterator getLevelOrderIterator();
25
CMPSCI 187
The BinaryTree Class:
getHeight
private int getHeight(BinaryNode node)
{ int height = 0;
if (node != null)
height = 1 + Math.max (
getHeight((BinaryNode)node.getLeftChild()),
getHeight((BinaryNode)node.getRightChild()));
return height; }
26
The BinaryNode Class:
CMPSCI 187
getNumberOfNodes


Number of nodes in a tree is 1 + number in
left tree + number in right tree
Another naturally recursive method
public Object getRootData();
public int getHeight();
public int getNumberOfNodes()
{return getNumberOfNodes(root);}
public int getNumberOfNodes();
public boolean isEmpty();
public void clear();
public void setTree(Object rootData);
public void setTree(Object rootData,
BinaryTreeInterface leftTree,
BinaryTreeInterface rightTree);
public Iterator getPreorderIterator();
public Iterator getPostOrderIterator();
public Iterator getInorderIterator();
public Iterator getLevelOrderIterator();
27
CMPSCI 187
The BinaryTree Class:
getNumberOfNodes
private int getNumberOfNodes(BinaryNode node)
{ int leftNumber = 0;
int rightNumber = 0;
if ((BinaryNode)node.getLeftChild() !=null)
leftNumber=getNumberOfNodes(
(BinaryNode)node.getLeftChild());
if ((BinaryNode)node.getRightChild() != null)
rightNumber=getNumberOfNodes(
(BinaryNode)node.getRightChild());
return 1+leftNumber+rightNumber;}
28
CMPSCI 187
The BinaryTree Class:
isEmpty, clear
public boolean isEmpty()
{ return root==null;}
public Object getRootData();
public int getHeight();
public void clear()
{ root = null;}
public int getNumberOfNodes();
public boolean isEmpty();
public void clear();
public void setTree(Object rootData);
public void setTree(Object rootData,
BinaryTreeInterface leftTree,
BinaryTreeInterface rightTree);
public Iterator getPreorderIterator();
public Iterator getPostOrderIterator();
public Iterator getInorderIterator();
public Iterator getLevelOrderIterator();
29
CMPSCI 187
The BinaryTree Class:
setTree
public void setTree(Object rootData)
{ root=new BinaryNode(rootData); }
public void setTree(Object rootData, BinaryTreeInterface leftTree,
BinaryTreeInterface rightTree)
{ privateSetTree(rootData, (BinaryTree)leftTree,
(BinaryTree)rightTree);}
public Object getRootData();
public int getHeight();
public int getNumberOfNodes();
public boolean isEmpty();
public void clear();
public void setTree(Object rootData);
public void setTree(Object rootData,
BinaryTreeInterface leftTree,
BinaryTreeInterface rightTree);
public Iterator getPreorderIterator();
public Iterator getPostOrderIterator();
public Iterator getInorderIterator();
public Iterator getLevelOrderIterator();
30
CMPSCI 187
The BinaryTree Class:
privateSetTree - attempt 1
private void privateSetTree(rootData, BinaryTree leftTree,
BinaryTree rightTree)
{
root = new BinaryNode(rootData);
if (leftTree != null) root.setRightChild(leftTree.root);
if (rightTree != null) root.setRightChild(rightTree.root);
}
Problems?
Call by reference for the left and right tree results in
the actual subtrees sharing nodes with the new tree.
Solution?
Make a copy of left and right tree before executing
the set methods above. But needs to be a deep
copy.
31
The BinaryTree Class:
CMPSCI 187
privateSetTree

Solution: set trees to null after assignment,
 Force
the user to copy the trees before calling
setTree if it’s necessary to preserve them

Solution: Don’t allow the operation
 There’s
nothing wrong with not allowing certain
operations, such as divide by zero.
32
CMPSCI 187
The BinaryTree Class:
privateSetTree - attempt 2
private void privateSetTree(Object rootData, BinaryTree leftTree,
BinaryTree rightTree) throws BinaryTreeException
{
root = new BinaryNode(rootData);
if (this == leftTree || this == rightTree) throw
new BinaryTreeException("Can’t create tree in privateSetTree");
if (rightTree == leftTree) throw new BinaryTreeException
("Can’t create tree in privateSetTree");
if (leftTree != null) root.setLeftChild(leftTree.root);
if (rightTree != null) root.setRightChild(rightTree.root);
leftTree = null;
rightTree = null;
}
Not consistent with our interface; also need to
write the exception class.
33
CMPSCI 187
BinaryTreeExceptions
public class BinaryTreeException extends Exception
{
public BinaryTreeException()
{}
public BinaryTreeException(String s)
{super(s);}
}
34
CMPSCI 187
Binary Tree Traversals
inorderTraverse
private void inorderTraverse(BinaryNode node)
{
if (node != null)
{
System.out.print("(");
inorderTraverse((BinaryNode)node.getLeftChild());
System.out.print(" "+node.getData()+" ");
inorderTraverse((BinaryNode)node.getRightChild());
System.out.print(")");
}
}
35
CMPSCI 187
Binary Tree Iterators

Constructor of the iterator pushes the tree nodes onto
a queue or a stack

The next method simply pops the stack to get the
next element

We’ll do a postorderIterator


You do the preorderIterator and inorderIterator
Can use our post order traversal methods to get the
iterator
36
CMPSCI 187
Binary Tree Iterators
postOrderIterator
public class PostOrderIterator
{ Stack s, temp;
public PostOrderIterator(BinaryTree t) throws StackFullException,
StackEmptyException
//pre: t != null
//post: this is an postorder Iterator for all the elements in t
// the first call to next() will return the first postorder element of t
{ s = new LinkedStack(); temp = new LinkedStack();
BinaryNode current = t.getRoot();
pushNodes(current); //push all nodes onto stack using postorder traversal
while(!temp.isEmpty()) //reverse node order since nodes have been
pushed in postorder
s.push(temp.pop());
}
37
CMPSCI 187
Binary Tree Iterators
pushNodes
private void pushNodes(BinaryNode n) throws StackFullException
{
if (n != null)
{
pushNodes((BinaryNode)n.getLeftChild());
pushNodes((BinaryNode)n.getRightChild());
temp.push(n);
}
}
38
CMPSCI 187
Binary Tree Iterators
hasNext, next
public boolean hasNext()
//post: Returns true iff this iteration has more elements
{ return !s.isEmpty(); }
public Object next() throws NoSuchElementException,
StackFullException, StackEmptyException
// pre: The structure of the tree this is iterating has not changed
//
since this was constructed.
// post: Returns the next element in the iteration.
// Throws a NoSuchElementException if !hasNext()
{ if (hasNext()) return s.pop();
else throw new NoSuchElementException(); }
}
39
CMPSCI 187
Binary Tree Iterators
remove
public void remove() throws
UnsupportedOperationException
//post: Throws an UnsupportedOperationException
//
(a runTime Exception)
// (Although defined in the java.util.Iterator interface,
// it is optional and we will not implement it)
{ throw new UnsupportedOperationException(); }
40
CMPSCI 187
The BinaryTree Class:
Other Useful Methods
public void postorderTraverse()
{ postorderTraverse(root);}
private void postorderTraverse(BinaryNode node)
{
if (node != null)
{ postorderTraverse((BinaryNode)node.getLeftChild());
postorderTraverse((BinaryNode)node.getRightChild());
System.out.print(node.getData());
}
}
41
CMPSCI 187
The BinaryTree Class:
Other Useful Methods
public void attachLeft(BinaryTree t)
{//pre: t is a non-null binary tree
//post: the left child of this tree is set to t
BinaryNode troot = t.getRoot();
root.setLeftChild(troot);
}
public void attachRight(BinaryTree t)
{{//pre: t is a non-null binary tree
//post: the right child of this tree is set to t
BinaryNode troot = t.getRoot();
root.setRightChild(troot);
}
42
CMPSCI 187
The Complete Implementation
Classes

Binary Node



Binary Tree [linked implementation]






TreeInterface.java
TreeIteratorInterface.java
BinaryTreeInterface.java
BinaryTree.java
BinaryTreeException.java
The Stack [linked implementation]







BinaryNodeInterface.java
BinaryNode.java
Stack.java
Node.java
LinkedStack.java
StackFullException.java
StackEmptyException.java
NoSuchElementException.java
Test Program

BinaryTreeTest.java
43
CMPSCI 187

The TreeNode Class
TreeNode has four class variables
 Reference
to the parent node
 The element stored there
 A list of children nodes
 A value field (for later applications)
TreeNode
Object
Object
NodeList
Parent
Element
Value
Children
header
X
TreeNodes!
trailer
X
44
CMPSCI 187
insertChild Method
Node C
trailer
••••
X
Node H
Parent:C
Element
Value
Children
trailer
header
X
X
Parent:H
Node I
Element
Value
Children
header trailer
X
X
45
CMPSCI 187


Enumerating the Children
Child node Enumerator
Implements the Enumeration interface
Parent
Element
Value
Children
header
X
trailer
X
public Enumeration children(TreeNode n)
{
return new ListEnumerator(n.getChildren());
}
46
CMPSCI 187
Balanced vs. Unbalanced Trees 1
start
A
B
root
C
A
F
B
G
C
L
D
E
F
G
D
H
I
J
K
L
H
I
Sort of Balanced
E
Mostly Unbalanced
J
K
47